Kristie Ferrentino

Graphing Linear Inequalities

in Two Variables

ADMIT TICKET

1. Find and graph the solution set of the inequality. 

2. Determine the equation of a line that passes through the point (2,6) and has a slope of 5.

162)2(4 xx

INEQUALITY VIDEO

OBJECTIVE

Students will be able to demonstrate their understanding of how to solve linear inequalities in two variables by graphing linear inequalities in two variables.

GRAPH LINEAR INEQUALITIES

Linear inequality graph: is a set of points in a coordinate plane that represent all of the possible solutions of that inequality We represent the boundary line of the

inequality by drawing the function represented in the inequality

Boundary Line: separates the coordinate plane into regions

GRAPHING LINEAR INEQUALITIES

Inequality Type of Line Shaded Region

> (greater than) Above

< (less than) Below

≥ (greater than and/or equal to) Above

≤ (less than and/or equal to) Below

Dashed Line

Dashed Line

Solid Line

Solid Line

GRAPHING LINEAR INEQUALITIES

Less than Less than and/or equal to

Greater thanGreater than and/or equal to

Inequality

STEPS TO GRAPHING INEQUALITIES

Remember: ≤ and ≥ will use a solid line

< and > will use a dashed line

Change the inequality sign to an equal sign; then graph the equation

Step 1:Change the

inequality sign, Graph the line

STEPS IN GRAPHING INEQUALITIES

Remember: If greater than, greater than and/or equal

to, shade above the inequality

If less than, less than and/or equal to, shade below the inequality

Can use a test point to check if the shaded part of the graph contains the inequality solutions.

Step 2: Determine which half of the graph should be shaded

STEPS TO GRAPHING INEQUALITIES

Shade the part of the graph that contains the solutions.

Step 3: Shade

EXAMPLE 1

Step 1: Change the

sign, and graph the line

Step 2: Determine which half of the graph should be shaded

Step 3: Shade

Use a graph to solve y≤ 2x + 3

EXAMPLE 1

Use a graph to solve y ≤ 2x + 3

y ≤

2x

+3

30

300

3)0(20

32

)0,0(

32

32

xy

xy

xyChange the sign

Test Point

Test the point in original inequalityTrue

EXAMPLE 2

Use a graph to solve y > -x + 4

EXAMPLE 2

40

4)0(0

4

)0,0(

4

4

xy

xy

xyChange sign

Test Point

Test the point in original inequalityFalse

y > -x +

4 Use a graph to solve y > -x + 4

PRACTICE PROBLEMS

Use a graph to solve the following inequalities

1. y < x -72. y ≥ -3x - 33. y> x4. y ≤ 2x - 4

WHAT DID WE LEARN TODAY?1. What kind of line is less than or greater

than?2. What kind of line is greater than or equal to

and less than or equal to?3. If the inequality is greater than, greater

than or equal to, what part of the graph is shade?

4. If the inequality is less than, less than or equal to, what part of the graph is shade?

5. What are the three steps to graphing linear inequalities?